[Maths Class Notes] on Cube Root of 3 Pdf for Exam

When we say the cubed root of 3, then it would mean 27. This is calculated as (3x3x3). When a number is cubed, it implies that it is multiplied itself by 3 times. So 3 cubes is 27. For example, If you have 7 to the power of 3 (or cubed, as 3 implies cubed in math) then to solve, I would say 7 multiplied by itself 3 times. 7x7x7, this comes out to be 343(7×7 is 49, and 49×7 is 343).

How to Determine the Cube Root of 3?

Before we proceed to learn finding the cube root of number 3, we have to first acquaint ourselves in knowing the cubes of the numbers stated below.

Number (x)

Cube of Number (x³)

Output (Perfect Cubes)

1

1×1×1

1

2

2×2×2

8

3

3×3×3

27

4

4×4×4

64

5

5×5×5

125

6

6×6×6

216

7

7×7×7

343

8

8×8×8

512

9

9×9×9

729

10

10×10×10

1000

11

11×11×11

1331

12

12×12×12

1728

13

13×13×13

2197

14

14×14×14

2744

15

15×15×15

Cube Root Lists

Below is a tabular form for the cube root of numbers from 1 to 15.

 Number Cube Root [sqrt[3]{n}] 1 1.000 2 1.260 3 1.442 4 1.587 5 1.710 6 1.817 7 1.913 8 2.000 9 2.080 10 2.154 11 2.224 12 2.289 13 2.351 14 2.410 15 2.466

Cube Root of 3 Explained

The cube root of any number n will be a number x, such as x³ = n. Thus, in order to identify the cube root of three, we are required to determine a number, which when multiplied three times with the number itself, provides the number 3, such as x³ = 3 or x = [sqrt[3]{3}]. Hence, we will here require finding the value of x.

The value of the cube root of 3, [sqrt[3]{3}], is equivalent to 1.44224957031. Seeing that 3 do not make a perfect cube, hence it is a bit difficult to determine its cube root. However, for perfect cubes like 8, 27, 64, 125 729 etc., the cube root of such numbers are whole numbers, since, 3³ = 3×3×3 = 27 and 5³ = 5×5×5 = 125. Therefore, the cube root of 125 is 5 and of 27 is 3.

Thus, for 3 in cubed, then you would multiply it 3 times. 3³ = 3x3x3; 3×3 is 9, and 9×3 is 27. Hence, the 3 cubed is 27.

Cube Root Symbol

The symbol of cube root is as ‘[sqrt[3]{}]’

Cube root can also be determined by the approximation method.

Step-By-Step Process to Find Cube Root Easily

Now, let us find out the value of [sqrt[3]{3}], in a detailed step by step manner.

Let us suppose that the cube root of 3 is equivalent to x.

Then, x = [sqrt[3]{3}]

1³ = 1 and 2³ = 8

Thus, x lies in between 1 and 8. But, it lies near to the number 1 than 8, if we observe in a number line. Therefore, we can presuppose a value; say 1.4, which could be an approximation to the cube root of 3.

Now, in order to identify the value of [sqrt[3]{3}], we are required to divide 3 by an approx value.

Dividing 3 by 1.4, we get

3/1.4 = 2.1428

Again, we need to divide this value by 1.4.

On dividing, we get,

2.1428/1.4 = 1.53

Now, taking the average of 1.4, 1.4 and 1.53 in order to obtain the value of [sqrt[3]{3}].

(1.4+1.4+1.53)/3 = 1.44

Thus, the actual value of [sqrt[3]{3}] = 1.442249.

Therefore, 1.44 is approximately equivalent to 1.442249.